Approximation algorithms for minimizing segments in radiation therapy

Luan, Shuang; Saia, Jared; Young, Maxwell

doi:10.1016/j.ipl.2006.10.003

Cited by 13 publications

(29 citation statements)

References 10 publications

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“…Bansal et al [4] provide a 24/13-approximation algorithm for the single-row problem. Most relevant to our current work, Luan et al [13] give two approximation algorithms for the full m × n problem; however, they do not confirm the performance of their algorithms with experiments. Finally, we note that other important metrics for treatment planning exist, such as total irradiation time (see [1,7,12]).…”

Section: Introductionmentioning

confidence: 78%

A note on improving the performance of approximation algorithms for radiation therapy

Biedl

Durocher

Hoos

et al. 2011

Information Processing Letters

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The segment minimization problem consists of representing an integer matrix as the sum of the fewest number of integer matrices each of which have the property that the non-zeroes in each row are consecutive. This has direct applications to an effective form of cancer treatment. Using several insights, we extend previous results to obtain constant-factor improvements in the approximation guarantees. We show that these improvements yield better performance by providing an experimental evaluation of all known approximation algorithms using both synthetic and real-world clinical data. Our algorithms are superior for 76% of instances and we argue for their utility alongside the heuristic approaches used in practice.

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Section: Introductionmentioning

confidence: 78%

A note on improving the performance of approximation algorithms for radiation therapy

Biedl

Durocher

Hoos

et al. 2011

Information Processing Letters

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“…Work by Collins et al [10] shows that the single-column version of the problem is NP-complete and provides some nontrivial lower bounds given certain constraints. Work by Luan et al [16] gives two approximation algorithms for the full Ñ ¢ Ò segmentation problem, and Biedl et al [6] extend this work to achieve better approximation algorithms that result in performance improvements.…”

Section: Related Workmentioning

confidence: 99%

Faster Optimal Algorithms for Segment Minimization with Small Maximal Value

Biedl

Durocher

Engelbeen

et al. 2011

Lecture Notes in Computer Science

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Abstract. The segment minimization problem consists of finding the smallest set of integer matrices (segments) that sum to a given intensity matrix, such that each summand has only one non-zero value (the segment-value), and the non-zeroes in each row are consecutive. This has direct applications in intensity-modulated radiation therapy, an effective form of cancer treatment.We study here the special case when the largest value À in the intensity matrix is small. We show that for an intensity matrix with one row, this problem is fixed-parameter tractable (FPT) in À; our algorithm obtains a significant asymptotic speedup over the previous best FPT algorithm.We also show how to solve the full-matrix problem faster than all previously known algorithms. Finally, we address a closely related problem that deals with minimizing the number of segments subject to a minimum beam-on-time, defined as the sum of the segment-values. Here, we obtain a almost-quadratic speedup over the previous best algorithm.

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“…Two versions of this model are presented and tested in the paper: with integer programming and with constraint programming. Luan et al (2007) present approximation algorithms for the unconstrained DC problem. They define matrices P k whose elements are the k th digits in the binary representation of the entries in A.…”

Section: Theorem 13mentioning

confidence: 99%

Mathematical optimization in intensity modulated radiation therapy

et al. 2009

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The design of an intensity modulated radiotherapy treatment includes the selection of beam angles (geometry problem), the computation of an intensity map for each selected beam angle (intensity problem), and finding a sequence of configurations of a multileaf collimator to deliver the treatment (realization problem). Until the end of the last century research on radiotherapy treatment design has been published almost exclusively in the medical physics literature. However, since then, the attention of researchers in mathematical optimization has been drawn to the area and important progress has been made. In this paper we survey the use of optimization models, methods, and theories in intensity modulated radiotherapy treatment design. This is an updated version of the paper that appeared in 4OR, 6(3), 199-262 (2008).

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Approximation algorithms for minimizing segments in radiation therapy

Cited by 13 publications

References 10 publications

A note on improving the performance of approximation algorithms for radiation therapy

A note on improving the performance of approximation algorithms for radiation therapy

Faster Optimal Algorithms for Segment Minimization with Small Maximal Value

Mathematical optimization in intensity modulated radiation therapy

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